"It makes sense [to translate "oder" as "or" here], since, I believe, the stickers are for each city, and having a sticker from one city doesn't necessarily mean you can enter another city...or does it?"

In fact, Germany has green, yellow, and red stickers for cars now, and those stickers apply across the nation. Wherever I get my green sticker, it is green throughout Germany – yet another example of how the Germans use "oder" incorrectly, thereby misleading readers.

Yes, you can use the same green sticker to get into downtown Munich, Stuttgart, Berlin, and (!) Heidelberg.

Coming in late but think you're missing something here. The oder is intended to indicate that "München, Stuttgart, Berlin oder Heidelberg" is not an exclusive list but that the author is just citing a few random examples.

If I saw "München, Stuttgart, Berlin und Heidelberg" in the German sentence, I would entertain the notion that these four cities are the only ones with Umweltzonen for some reason. This might well be different in English -- I often find myself replacing English ands with German oders in my own translations. But as long as we all know what we're doing in our target/native languages, I don't see a problem.